The problem of sound reinforcement Kirkhoff plates on the main directions of strain and stress in the pure elastic and elastic-plastic transverse bending. Additionally profiling formulated task management such constructions, provided that the fibers of one of the families equal-stressed on the front surface of the plate. A qualitative analysis of the relevant systems of governing equations. The possibility of the existence of several alternative solutions to this problem that can be controlled. The concrete calculations showing that through rational profiling of bent plates consumption phase materials in them can significantly (several times) lower compared to reference designs.